CBSE

Exercise 1.3 1. Make correct statements by filling in the symbols or in the blank spaces: (i) {2, 3, 4} _______ {1, 2, 3, 4, 5} (ii) (iii) { is a student of class XI of your school} _______ { student of your school} (iv) { is a circle in the plane} _______ { is … Read more

Exercise 7.1 1. How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that: (i) repetition of the digits is allowed (ii) repetition of the digits is not allowed. Ans. (i) The unit place can be filled by any one of the digits 1, 2, 3, 4 and … Read more

Exercise 10.2 In Exercises 1 to 8, find the equations of the line which satisfy the given conditions: 1. Write the equations for the and axis. Ans. Equation for axis is Equation for axis is 2. Passing through the point with slope Ans. Given: and 3. Passing through (0, 0) with slope Ans. Given: and … Read more

Exercise 1.5 1. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find: (i) A’ (ii) B’ (iii) (A C)’ (iv) (A B)’ (v) (A’)’ (vi) (B – C)’ Ans. Given: U = … Read more

Exercise 7.2 1. Evaluate: (i) 8! (ii) (ii) 4! – 3! Ans. (i) 8! = = 40320 (ii) 4! – 3! = = 24 – 6 = 18 2. Is 3! + 4! = 7!? Ans. L.H.S. = 3! + 4! = = 6 + 24 = 30 R.H.S. = 7! = = 5040 L.H.S. … Read more

Exercise 10.3 1. Reduce the following equations into slope-intercept form and find their slopes and the intercepts. (i) (ii) (iii) Ans. (i) Given: ……….(i) Comparing with we have and (ii) Given: ……….(i) Comparing with we have and (iii) Given: ……….(i) Comparing with we have and 2. Reduce the following equations into intercept form and find … Read more

Exercise 3.1 1. Find the radian measures corresponding to the following degree measures: (i) (ii) (iii) (iv) Ans. (i) (ii) (iii) (iv) 2. Find the degree measures corresponding to the following radian measures . (i) (ii) (iii) (iv) Ans. (i) = (ii) = (iii) (iv) 3. A wheel makes 360 revolutions in one minute. Through … Read more

Exercise 7.3 1. How many 3-digit numbers can be formed by using the digits 1 to 9 if no digits is repeated? Ans. Total number of digits = 9 and Number of digits used without repetition = 3 Number of permutations = = = 504 2. How many 4-digit numbers are there with no digit … Read more

Miscellaneous Exercise 1. Find the values of K for which the line is: (a) parallel to the axis (b) parallel to the axis (c) passing through the origin. Ans. Given: Equation of line (a) If the line parallel to axis, then (b) If the line parallel to axis, then (c) If the line passes through … Read more

Exercise 3.2 Find the values of other trigonometric functions in exercises 1 to 5. 1. lies in third quadrant. Ans. Given: [ lies in third quadrant] Now, 2. lies in second quadrant. Ans. Given: [ lies in second quadrant] Now, 3. lies in third quadrant. Ans. Given: [ lies in third quadrant] Now, 4. lies … Read more

Exercise 7.4 1. If find Ans. Given: 2. Determine if: (i) (ii) Ans. (i) Given: (ii) Given: 3. How many chords can be drawn through 21 points on a circle? Ans. There are 21 points on the circumference of a circle. Since one and only one chord can be drawn by joining 2 distinct points, … Read more

Exercise 11.1 In each of the following Exercises 1 to 5, find the equation of the circle with: 1. Centre (0, 2) and radius 2. Ans. Given: and Equation of the circle = 2. Centre and radius 4. Ans. Given: and Equation of the circle = 3. Centre and radius Ans. Given: and Equation of … Read more

Exercise 3.3 Prove that: 1. Ans. 1. L.H.S. = = = R.H.S. 2. Ans. L.H.S. = = = = = 3. Ans. L.H.S. = = = = = = R.H.S. 4. Ans. L.H.S. = = = = = = R.H.S. 5. Find the value of: (i) (ii) Ans. (i) = (ii) = = Prove the … Read more

Miscellaneous Exercise 1. How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER? Ans. There are 8 letters in the word DAUGHTER. In this word 3 vowels and 5 consonants. 2 vowels and 3 consonants are to be selected. Number of … Read more

Exercise 11.2 In each of the following Exercises 1 to 6, find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum. 1. Ans. Given: Equation of parabola Comparing with we have Coordinates of focus are (3, 0). Axis of parabola is Equation of … Read more